m^2-m=2/3

Solution for m^2-m=2/3 equation:

m^2-m=2/3

We move all terms to the left:

m^2-m-(2/3)=0

We add all the numbers together, and all the variables

m^2-m-(+2/3)=0

We add all the numbers together, and all the variables

m^2-1m-(+2/3)=0

We get rid of parentheses

m^2-1m-2/3=0

We multiply all the terms by the denominator


m^2*3-1m*3-2=0

Wy multiply elements

3m^2-3m-2=0

a = 3; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·3·(-2)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{33}}{2*3}=\frac{3-\sqrt{33}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*3}=\frac{3+\sqrt{33}}{6}
$